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Explanation of the Rainbow.

the sphere of view. There is also frequently seen external to this bow a second, having a much fainter light, of greater diameter than the first, and with the colours in a reverse order, i.e., red in the inner and violet on the outer border.

The explanation of this interesting phenomenon is as follows :— While the sun shines upon the spherical drops of falling rain, the light entering the whole central part of any drop passes completely through, but that portion which enters obliquely near the edge of the upper part of the drop, as at a (fig. 227), is refracted or bent, and much of it reaches the back surface of the drop at y so slantingly, or at such an angle, that it suffers there entire or total reflection

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(Art. 892), instead of being transmitted; the ray, therefore, is returned to b, where it escapes from the drop, and as here shown, descends to the earth or eye in the direction be. Thus every drop of rain on which the sun shines is a little spherical mirror suspended in the sky, and is returning, at cerFig. 227. tain angles, a portion of the light which falls upon it; and an eye placed in the required direction, receives the reflected light. If in this case, however, there were reflection only, and no refraction with separation of colours, the rainbow would be only a very narrow resplendent arc of white light, formed by millions of little mirrors in the sun; but, in truth, as the light which enters near the edge of the drop, traverses the surface very obliquely, it is much bent or refracted at a before its reflection at y, and afterwards at b, and is divided into rays of its seven colours, as it would be on passing through a prism. (See Art. 812.) In consequence of this division or separation of the

20 3 a 40

60.

70

Fig. 228.

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3

2

light, as it escapes from the drop

at b, instead of one white ray descending from each drop to a certain point of the earth, seven rays descend (marked by dotted lines from the figure I on the left hand to 7, 6, 5, &c., on the right, fig. 228). The separation in the drawing is made greater than occurs in reality, in order to render the fact

more evident. Of these coloured rays, an eye can only receive one at a time from the same drop, which drop will then appear of the

Production of the Colours.

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colour of the ray; but for the same reason that seven eyes placed in a line from above downwards, as at 7, 6, 5, &c., on the right, would be required to see the seven colours from one drop in the bow, so one eye looking in the direction of seven drops situated in a corresponding row, as from I to 7 on the left, will catch the lower or red ray of the upper, the orange or second ray of the next, the yellow or third ray of that which follows, and so on, while it will lose all the others, and thus will see the several drops as if they were each of one colour only. Of such elements, then, found in the same relative directions all around the sky, the arch or bow is constituted. Each colour emerges at a definite angle, and all the drops emitting the red ray at the same angle, will necessarily take the form of a circle or bow, of which the eye of the spectator will be the centre. So of the other colours in their order. If the reader will imagine a cone, of which the apex is in the eye, and the base more or less elevated above the horizon, according to the position of the sun, he will at once comprehend why each colour takes the form of a bow, and why the colours are in concentric layers.

S

894. The annexed illustration from Pouillet (fig. 229), will show the exact relation of the eye of the spectator to the rays from the sun, incident on and emerging from the drop. O represents the spectator with his back to the sun, and OH a horizontal line passing from the centre of the sun through the eye of the spectator, and carried to infinity towards the east. The line, o T, passing from the eye of the spectator, is carried to infinity in the raincloud. This forms, with the horizontal line, O H, an angle of 42° 1' 40". Let it be supposed that this second line turns around the first and preserves the same angular relation, it will describe a conical surface, of which the

E

Fig. 229.

H

upper half only requires notice. The line in each of its positions will meet with a number of drops of rain, and A B C represents one of these drops. The rays of light which it receives from the centre of the sun are horizontal, and parallel to O H. The ray

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Inner and Outer Bows.

S A, after having undergone refraction in A, reflection in B, and a second refraction in C, issues from the drop in the direction C E, at its maximum angle of deviation; S A being parallel to O H, the angle, S T E, is 42° 1′ 40′′, like the angle, E O H. Under these conditions the spectator will see the red ray only in the drop, and in all the drops equidistant from the eye of the spectator.

Just as no circle can have two centres, so no two persons can see the same rainbow. Even one person by looking separately with his two eyes sees two different bows, and the same eye does not for two instants, receive coloured rays from the same drops.

895. We have here described what is called the inner or principal bow, formed in the drops by two refractions, and one reflection, of

light. To produce the fainter second or outer bow, mentioned above, and of which the colours are in a reverse order, the light which enters on the under size of the drop, as at a, is reflected first at y, then again at b, and escapes at c towards the eye, after two reflections, as well as two refractions. Owing to there being two reflections, there is a greater loss of light, and therefore less intensity of colour in the outer bow; and as its diameter is 108°, a portion of it may be visible when the inner bow cannot be seen.

Fig. 230.

In the outer bow, the colours appear in an inverted order, owing to the rays of light entering the drop from below, while in the inner bow they enter from above. Hence in the outer bow the violet is always on the outside, while in the inner it is on the inside. The reds are, therefore, near to each other in the two bows. The breadth of the outer bow is equal to 3° 10′, nearly three times that of the inner, and the space between the two bows is 8° 57'.

Rainbows are never seen at mid-day, or when the sun is high above the horizon. As the sun, the eye of the spectator, and the centre of the bow are always in a right line, it follows that more than a semicircle can never be seen, and this can only be seen at the rising or setting of the sun-this luminary and the centre of the bow being then in a horizontal line. The higher the sun, the smaller the portion of the semicircle seen; and when the sun is more than 42° 18′ above the horizon, the inner or brighter bow entirely disappears, as its centre would then be so many degrees below the horizon. For a similar reason, when the sun has an altitude of 54° 23', the outer and paler bow is no longer seen.

The Solar Spectrum.

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On some rare occasions a third bow has been seen, but owing to the increased number of reflections which the light then undergoes, the colours have been very faint.

An artificial rainbow may be produced in sunshine at any time by scattering water into drops from a whirling brush or otherwise, on the side away from the sun, at a moderate height; and a rainbow is often seen in the spray of fountains, of a lofty waterfall, or of waves in a storm. The cut-glass ornaments of chandeliers produce colours on the same principle as rain-drops. Mist and particles of frozen water between a luminous body and the eye produce the circular halos with little colour often observed round the sun and moon. A colourless halo is light reflected from the external surfaces of drops or solid particles.

The Solar Spectrum and Spectrum Analysis.

896. We have already (Art. 812) mentioned the beautiful experiment made by Newton in 1675, of unravelling the thread of white light, and showing it to be really composed of a number of different coloured threads. Since the days of Newton, this decomposition of light has developed into one of the most attractive and instructive subjects in the whole field of physical science. It has become an instrument in the hand of the chemist to detect the existence of metals, where other means of detection would utterly fail; it has even revealed the composition of the sun and fixed stars—a feat in chemistry more incredible, at first appearance, than would be the realization of the wild dream of the alchemist. It is necessary,

therefore, that we should enter somewhat more minutely into the experiment of Newton, and spectrum analysis, in connection with the wave or undulatory theory of light.

There are, according to the latter doctrine, incessantly beating upon our globe countless millions of ethereal waves, having their prime source in the sun, and wafting to our world all the life and beauty which it contains. These ether waves are not all of one size and rate of motion, but of very varied length, and of correspondingly varied effect. Waves within the limits of length mentioned (Art. 914) affect the optic nerves producing the sensation of light; slower and longer ether waves (within other limits) communicate to ponderable molecules those vibrations which excite in us the sense of heat; while, again, ether-waves, within certain higher limits than those of light waves, are specially adapted to excite those atomic changes or motions which are called chemical.

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Prismatic Decomposition of Light.

897. It follows at once from the conception of wave-motion, and of its being retarded on passing from a rarer to a denser medium, that a prism-shaped dense medium will bend a short rapid wave more out of its original course than a long and slow one. If, then, the ether waves, poured on our earth by the sun, be of different lengths, a little consideration will show that a beam or a bundle of such waves, SP (fig. 231), falling upon a prism, P, will be assorted according to wave-lengths, and displayed in a long strip, V R., of the same breadth

as the image of the sun would be, in falling on the screen without refraction. Different lengths of ether-waves exhibit themselves to the eye as the different rainbow colours, violet, indigo, blue, green, yellow, orange, red; but, by special means of detection, it is found that beyond the visible violet rays of the solar spectrum there are invisible rays having a powerful chemical effect, and beyond the red end of the visible spectrum there are invisible waves of ether having a powerful heating effect. It is found that the rays which affect the eye most strongly are not those which affect a sensitised piece of paper most, or which affect a delicate thermometer

most.

898. The diagram (fig. 232) will show how far the spectrum really extends on each side of the visible or coloured spectrum whose dark lines are inserted as an index. It also shows the distribution of the chemical, luminous, and heating power of a beam. The greatest luminous intensity falls near the D or sodium line (see Art. 904) ; the maximum heating effect lies outside the red end of the visible spectrum, while the greatest chemical effect lies in the violet of the opposite end.*

* Roscoe's 'Spectrum Analysis,'